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# Aptitude - Time and Work - Discussion

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"Do not wait for leaders; do it alone, person to person."
- Mother Teresa
4.

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

[A]. 20 days[B].
 22 1 days 2
[C]. 25 days[D]. 30 days

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

 If difference of time is 60 days, B takes 3 x 60 = 90 days. 2

So, A takes 30 days to do the work.

 A's 1 day's work = 1 30

 B's 1 day's work = 1 90

 (A + B)'s 1 day's work = 1 + 1 = 4 = 2 30 90 90 45

 A and B together can do the work in 45 = 22 1 days. 2 2

 Rajender said: (Wed, Jun 16, 2010 08:27:14 AM) Please tell me how you have calculated differece of time 2 days.

 Sundar said: (Mon, Jul 5, 2010 07:59:13 AM) Hi Friends! The statement "A is thrice as good as workman as B" states that, If A complete a work in 1 day, B will take 3 days to complete the same work. Therefore, if A takes 1 day, B takes 3 days, the time difference is 2 days. If the time difference is 2 days, B takes 3 days to complete the work. Similarly if the time difference is 60 days, then B takes (3/2*60) = 90 days. Then A takes 90 - 60 = 30 days to complete the work. It is very simple man.

 Kumar said: (Mon, Jul 5, 2010 08:21:34 AM) Hi Guys, Let me do the same thing with different values. Given statement : "A is thrice as good as workman as B" Time difference : 60 days. If B takes 12 days to complete a work, A will take only 4 days to complete the same work. So, B takes 12 days whereas A takes 4 days only (because A is thrice as good as B). Here time difference is 12 - 4 = 8 days. If the time difference is 8 days, B takes 12 days. Similarly if the time difference is 60 days, then B takes (12/8 * 60) = 90 days. ...Rest thing you can understand from the explanation part.

 Bharathi said: (Fri, Jul 9, 2010 08:17:23 AM) Dear Friends, In this question atlast we got (a+b)'s 1 day work=2/45. How it is changed to be an A and B are together can do the work in 45/2.

 Nagu said: (Mon, Jul 12, 2010 02:55:48 AM) Hi Bharathi, If A takes 10 days to complete a work means A's one day work is 1/10 so complete this work A takes 10/1 days is same as 10 days Sat the same way (A + B)'s 1 day's work 2/45 means They will take 45/2 = 22 1/2 days I think you got my point have a nice day

 Sheetal said: (Tue, Aug 3, 2010 05:55:57 AM) Hi Guys, Don't be confused in data given in question. I have one short cut to solve such kind of question. A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1. SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA. K * X / K'S SQUARE - 1 =3 * 60 / 9 - 1 =3 * 60 / 8 =180 / 8 =22.5 DAYS AS MENTIONED OPTION B. I HOPE U WILL UNDERSTAND THIS THING & WILL APPLY IN QUESTION BASED ON THIS. All the best. Have nice day!

 Sangeetha said: (Wed, Aug 4, 2010 05:01:40 AM) Oh thanks sheetal

 Indhu said: (Wed, Sep 1, 2010 01:31:37 PM) Hi friends,. Though content is big it is easy to understand. Work done by A as compared to B=3:1. Time taken by A as compared to B=1:3. So, time difference is 2. A will finish the work 60 days lesser than B. Therefore time difference is 60. Time taken for A = 60/2 = 30. Hence time taken for B=3* time taken by A = 90. If A+B can do a piece of work in n days, then (A+B) 's 1day's work=1/n. Working together (A+B) 's one day work = (1/30) + (1/90) =2/45. If (A+B) 's 1day's work=1/n, then A+B can finish the work in n days. Therefore total time taken = 45/2= 22. 5 Days.

 Prashant said: (Wed, Sep 15, 2010 12:25:09 AM) Suppose B takes x days to finish the work and then according to question A will take (60-x) days to work. in question the ratio of time taken is 1:3 therefore 1/3= (60-x)/x x=45 So A can complete the work in (60-x)=(60-45)=15 days So (A+B) one day's work =(1/15 + 1/45) =4/45 So (A+B) complete the work in 45/4 = 11 1/4 days.

 Sugumaran said: (Wed, Sep 22, 2010 12:02:06 AM) Ratio of time taken=1:3 A finish the work in 60 days and B in x days. 1:3::60:x x=180 days So, A and B 1'days work 1/60+1/180=45 days Is it correct or not?

 M.Atul said: (Thu, Sep 23, 2010 05:54:37 AM) @Sugumaran please read carrefully problem. Though you have got same answer but it doesn't satisfied second condition that differnce in day should be 60 not 120.

 Priya said: (Thu, Sep 23, 2010 11:58:14 AM) Please tell me why we are taking 3/2 to multiply with 60. Please explin me.

 Harsha said: (Wed, Oct 13, 2010 08:29:53 AM) A clear approach: Given: A's time taken:B's time taken=1:3 So A's proportion of time taken=1/(1+3)=>1/4*some x B's proportion of time taken=3/(1+3)=>3/4*some x As it is said that difference of time is 60 days B's time-A's time=60 => 3x/4-x/4=60 =>x=120 So A's proportion of time taken =x/4=120/4=30 days B's proportion of time taken =3x/4=3*120/4=90 days A's 1 day's work = 1/30 B's 1 day's work = 1/90 (A + B)'s 1 day's work = (1/30 + 1/90)= 4/90=2/45 A and B together can do the work in 45/2 = 22 1/2 days.

 Naveen said: (Tue, Oct 26, 2010 09:37:38 AM) Hi, in prashanth answer, he equals the ratio 1/3 to 60-x/x but it actually x-60/x.

 Shilpi said: (Thu, Nov 18, 2010 09:18:05 AM) Can you pls teach me this equation 1/30+1/90=4/90

 Ashirwad said: (Sat, Nov 27, 2010 04:49:49 PM) HI FRIENDS THIS IS THE simplest method for solving this type of que.... K*S/(A^2-1) where S=DAYS FOR FINISHING WORK(60 GIVEN IN QUE) K=3 GIVEN IN QUE

 Ashirwad Dubey said: (Sun, Nov 28, 2010 02:48:59 PM) Hi friends k*x/(k^2-1) k=3 x=60 given in que ok friends

 Vikas said: (Wed, Dec 29, 2010 10:08:25 AM) I didnt understand how did we get that (3/2)*60 ?

 Showry said: (Wed, Jan 5, 2011 02:10:11 AM) Hi Friends, A:B=1:3 time taken.........since A is 3 good as B A takes 60 days less than B B-60:B=1:3............ i.e B-60/B=1/3..... B=90 days.... A=30...... (A+B)'s one day work (1/30+1/90) = (2/45) Total work by (A+B) is 45/2 i.e 22 1/2.............

 Gowri said: (Sat, Jan 8, 2011 05:34:53 AM) kl/(k)^2-1 k=3 l=60 3*60/(3)^2-1 =45/2 =22.5

 Nagarjun said: (Thu, Jan 13, 2011 11:46:43 PM) @Vikas Its just cross multiplication. If the difference is 2 days then b takes 3 days If the difference is 60 days then b takes x days Hence, x= (60*3)/2. I think you got it now.

 Naresh Kumar said: (Tue, Jan 18, 2011 04:11:52 AM) Thank you guys.

 Malini said: (Wed, Jan 19, 2011 07:49:13 AM) Sheetal thanks a lot dear. This short cut is very much easy.

 Baskar said: (Fri, Jan 21, 2011 12:29:40 AM) @bharathi i think u r in confusion.. just know dat work = day.. 1 day = 2/45 works.. in ques ask abt "work"? den cross mul 1 work = 45/2 days.. now u got it

 G.P. said: (Thu, Feb 10, 2011 04:32:14 AM) SIMPLE AND BEST WAY since a is thrice better than b hence a:b=1:3 similarly a takes 60 days less than b hence a:b=(b-60):b=1;3 cross multiplication n we get 3b-180=b hence b=90days hence a=30days 1/90+1/60=4/90 hence total daysreciprocal 90/4=45/2

 Nishant said: (Thu, Feb 10, 2011 11:53:34 AM) @ G.P. Thanks. I like the way you solve it.

 Balaji said: (Sat, Feb 19, 2011 12:11:16 AM) Showry you explained superbly.

 Prathyusha said: (Mon, Feb 28, 2011 08:30:19 PM) SIMPLE AND NICE EXPLANATION!... @KUMAR

 Vani said: (Fri, Mar 18, 2011 10:30:40 PM) Showry's explanation is good.

 Siva said: (Thu, Apr 21, 2011 01:38:29 PM) Hi Guys, I think following simple method (alternate) will make you more clear, A can complete work in N days => A's 1day work = (1/N)----1 B can complete work in n days => B's 1day work = (1/n)----2 Given data, A thrice as B so , A=3B A complete work 60 days less than B so, (N=n-60) Apply in 1 & 2 A's 1day work = (1/(n-60))-----3 B's 1day work = (1/n)--------4 we know that A=3B ; B=(1/n) so,Apply B in A we get[A=3/n] Apply in 3 3/n=(1/(n-60)) by solving, 3n-180=n n=90 so, B can complete work in 90 Days => B's 1 Day work =(1/90) we know that N=n-60, so, A can complete work in 30 Days => A's 1 Day work = (1/30) (A+B) 1 Day work = (1/30 + 1/90) by solving we get, A+B 1 Day work = 2/45, so A and B together can complete work in 45/2 Days.

 Hindu said: (Sat, Jun 25, 2011 09:32:33 PM) Hai sheetal your shortcut method helps lot to understand so quickly its really super.

 Naveen Kumar said: (Fri, Jul 1, 2011 01:18:59 AM) Hi friends, Here is a simple technique to calculate the above problem.... Given, If the If difference of time is 2 days, B takes 3 days. If difference of time is 60 days, B takes......? We can represent the above relation like this, 2------->3 60------>....? By cross multiplying the above terms we will get... 60*3/2 = 90. Note:- Always individual term should come in the denominator. By applying the above procedure you can solve any problem of this type.... I think this technique will help you while doing with this type of problems...

 Abdul said: (Sat, Jul 9, 2011 03:15:31 AM) Hey Siva your way of solving is fantastic and understandable! Thanks.

 Jezan said: (Sun, Jul 17, 2011 01:04:20 PM) According to this question if A is x, B will be x+60 1/3=x/x+60 3x=x+60 2x=6 x=30 A+B'S ONE DAY WORK=1/30+1/90=2/45 SO WHOLE WORK S= 45/2( UPSIDE DOWN) 22.5 DAYS. HOPE ALL LL GET DIS

 Jaswinder Singh said: (Sun, Aug 14, 2011 10:48:44 AM) Ratio of times taken by A and B = 1 : 3. or 1x:3x so, we say 3x-1x=60, 2x=60, x=30, so A will 30 day to complected a work, B will be complete the work ie 3x, 3(30)=90days, (A+B) 1 Day work = (1/30 + 1/90) by solving we get, A+B 1 Day work = 2/45, so A and B together can complete work in 45/2 Days.

 Sharan said: (Sun, Aug 21, 2011 11:08:37 PM) @Jaswinder singh: I understood your explanation man. Thanks.

 Sundar said: (Mon, Aug 22, 2011 11:13:44 AM) @All (Must read if you have any doubts) If B takes 3 days then A takes 1 day to complete the task. Time taken Ratio => A : B = 1 day : 3 days. 1 3 (difference is 2) 10 30 (diff 20) 30 90 (diff 60) <= Here diff is 60 days, So this is the correct ratio to be used in calculation, since it was mentioned in the given question. A alone can finish the task in 30 days. B alone can finish the task in 90 days. Work done by A alone in 1 day = 1/30 Work done by B alone in 1 day = 1/90 Work done by A and B in one day (1/30 + 1/90) = 3+1/90 = 4/90 The no. of days required to complete the task by A and B is = 90/4 = 22.5 days. ////**** Important Note: ****//// We cannot take other ratios like 1:3, 10:30, 40:120, 60:180 for the calculation. Since the diff is mentioned as 60 days. Because, it will give different answers for each different ratios used for calculation. If we take 1:3 => (1/1 + 1/3) = 4/3 If we take 10:30 => (1/10 + 1/30) = 4/30 If we take 40:120 = (1/40 + 1/120) = 4/120 If we take 60:180 => (1/60 + 1/180) = 4/180 ... so on. I hope this will help you. Have a nice day!

 Deepti said: (Thu, Aug 25, 2011 02:00:08 PM) It is not so big and easy to understand. let work done by B in 1 day = 1/x so work done by A in 1 day = 1/(x-60) 1/(x-60) = 3/x so x = 3x - 180 x = 90 work done by A and B in 1 day is 30 and 90 respectively work done by both together in 1 day = 1/30 + 1/90 = 2/45. total work done = 45/2

 Harsha said: (Thu, Sep 1, 2011 06:07:42 PM) Easy method : A can completed in x days B can in 3x days then A = B-60 (A can do in 60 days less than B ) => x=3x-60 => x= 30 => A=30, B=90 Then together work done is (1/30+1/90) = 2/45. Finally total work done is 45/2.

 Pinky said: (Sat, Sep 10, 2011 02:31:05 PM) @Sheetal superb explanation.

 Praveen said: (Fri, Sep 16, 2011 12:48:52 PM) Nice exp. Harsha.

 Nitin Singla said: (Fri, Sep 23, 2011 02:20:08 PM) Hey its simple to understand. Days taken by B = x Days taken by A= x - 60 Their time taken proportio is 1:3 so, x - 60/ x = 1/3 x=90; So A will do the work in = 30 days abd B in 3x= 3*30=90 days, and u can find their 1 day's work and ad it. Simple :)

 Srinivas said: (Sun, Sep 25, 2011 10:43:31 AM) Hi friends, Given A:B=1:3 Therefore B=3A--------equation 1 let B can do a work in x days. then A can do the same work in (x-60) days. then B=3A x=(x-60)3 therefore x=90 days therefore B can do a work in 90 days. and A will do a work in 90-60=30 days.

 Pavethra said: (Thu, Sep 29, 2011 02:15:30 PM) I tell that A is thrice as good as B so it should be 3:1 na. Am I right?

 Sunil Reddy said: (Tue, Oct 4, 2011 01:23:52 AM) We can use a simple formula here:[(KL)/k squqre-1)] -->here K=3(efficiency),L=60(time) so (3*60/(3*3)-1)=>180/8=221/2

 Vinod Reddy said: (Mon, Nov 7, 2011 02:30:10 PM) THANK U SHEETAL,your short cut method is simply super.there is no words to say

 Sundar said: (Fri, Nov 18, 2011 08:45:44 AM) If difference of time is 60 days 3*60/2 = 90 days. I can't get this step? Please explain.

 Riyaz said: (Wed, Nov 23, 2011 09:31:52 PM) Ratio of times taken by A and B = 1 : 3. That is If A takes 1 day B takes 3 days Time Difference is 3-1 = 2 days Here is the tricky part : If A takes 1/2 day B takes 3/2 days Time Difference is 3/2 - 1/2 = 1 days When time difference is 60 days (Just mulitply by 60) A takes 60/2 and B takes 3*60/2 So, A takes 30 days to do the work. and B takes 90 days to do the work. A's 1 day's work = 1/30 B's 1 day's work = 1/90 (A + B)'s 1 day's work = (1/30 + 1/90)= 4/90 = 2/45 A and B together can do the work in 45/2 = 22+1/2

 Anu said: (Sun, Nov 27, 2011 05:05:31 PM) Awesome explanation HARSHA

 Brajesh Anuragi said: (Mon, Nov 28, 2011 01:13:34 PM) Thanks Showry for given the simple and correct ans.

 Gauarv said: (Tue, Dec 27, 2011 08:59:05 PM) Thanks harsha.

 Neeraj said: (Sun, Jan 8, 2012 10:25:01 PM) A will finish the work 60 days lesser than B. What is it mean please explain?

 Abhay said: (Tue, Jan 10, 2012 07:49:42 PM) @Neeraj-A will finish the work 60 days lesser than B,means if B takes 60 days to complete the work,A takes 1 day.

 Sureshkumar said: (Thu, Jan 19, 2012 03:29:49 PM) Another easy way 2 find out: 1st put the ratio i.e.1:3(A:B) 2nd the condition given here is A can work less than 60 days So, find out the probability that matches with the ratio condition(A&B must be difference 60 here) for eg:let we take as A as 20 therefore B must be 60(here we get the difference as 40 only)according to 1:3 which cant satisfy The given condition(A less than B by 60 days) suppose you take A as 30 means you get B as 90 which is greater than 60 days of A....A=30 B=90 A's 1 day work=1/30 B's 1 day work=1/90 A+B's 1 day work =1/30+1/90=4/90 here they are not given to find out as 1day work...so take as 90/4=22.5 <==> 22(1/2).

 Varma said: (Thu, Jan 26, 2012 05:04:15 PM) Nice formula @Sheetal.

 Aarush said: (Thu, Feb 16, 2012 02:31:54 PM) Thanks sheetal.

 Raman(Uiet,Kuk) said: (Fri, Feb 17, 2012 03:33:34 PM) Guys check this out and don't be confused.... as we know A is 3 time better than B and A takes 60 days less than B so, time taken by A: time taken by B= 1:3 = b-60:b ( suppose time by B is b) by cross multiply, 3b-180=b i.e. b=90 so time taken by B=90 and time taken by the A is=90-60= 30

 Tabish said: (Sat, Feb 18, 2012 07:52:25 AM) @sheetal do not able to understand how you get that formula to calculate the time i.e. K*X/K^2-1

 Kapil said: (Mon, Feb 20, 2012 11:13:10 AM) Nic Explanation. . .Sheethal. . .

 Shro said: (Mon, Feb 20, 2012 09:41:37 PM) Indhu very easy simple explanation as per the question. Good :) thanku :)

 Sindhu said: (Thu, Feb 23, 2012 05:20:54 PM) HI, This method I feel to be quiet easier. A is thrice as good as workman as B. therfore, A=3B -(1) finish a job in 60 days less than B 1/B=60+1/A -(2) i.e B`s One day work = A`s one day work + 60 days. Solve (1) & (2) we will get A= 90; From (1) B=A/3 => B= 30. (A+B)`s 1 day work = 1/90+1/30 =2/45 =22 1/2 days

 Iyappan said: (Thu, Apr 12, 2012 10:33:40 PM) Naveen kumar your explanation is beautiful for me.

 Sanchi said: (Sun, Jun 3, 2012 09:59:54 PM) Very simple way. 3A=1B B takes x days. 3 (x-60) =x 3x-x=180 X dats is B=90, A=30. Now, 1/90+1/30=22. 5.

 Nitin Singh Parihar said: (Thu, Jul 5, 2012 04:04:43 PM) Let B do the work in 'x' days. So, A will take (x-60) days. Now, ratio of A:B=1:3 (given in ques). So, 1/3=x-60/x. => x=90 (B's 1 day work). So, A's work=30 days. Working together=1/30+1/90. =45/2 days. Easy and simple.

 Akansha said: (Tue, Aug 7, 2012 03:21:23 PM) B takes 3 times more days than A. i.e. B=3A. So. B-A=60. 3A-A=60 =>. A=30. B=90. Now calculate 1 day work of A and B.

 Sunny said: (Sun, Aug 26, 2012 09:48:54 PM) A is thrice as good as workman as B means 1:3(Ratio) Therefore A is able to finish a job in 60 days less than B So A= 1/60 and B=1/60 .....(Given) According to the ratio A=1/60 B=1/3*60 (As we are calculating by days) So Now A = 1/60 < B = 1/90 (A finishes work less than B) Working together, they can do it in: 1/A+B = 1/60 + 1/90 (As we are calculating by days)) 1/A+B = 2/45 So A+B = 45/2 Days Option (B) is the correct ans

 Vidya said: (Mon, Aug 27, 2012 10:38:17 PM) Can you please solve this using unitary method. Its b'coz I follow that method.

 Anji said: (Tue, Sep 4, 2012 08:12:43 PM) Let the time taken by A be x days, then time taken by B will be 3x days. Given that, time taken by A to finish the work = time taken by B -60 i.e, x=3x-60 => x=30. Therefore, time taken by A to finish the work is 30 days. so B takes 90 days. Now ,work done by A & B in 1 day=1/30 + 1/90 =4/90 =2/45 Time taken by A & B to complete the work=45/2 days =22 1/2 days

 Sanjeev said: (Tue, Sep 11, 2012 10:01:09 PM) #include void main() { float a,b; int c,d; printf("enter ratio of A : B\n"); scanf("%f",&a); printf("enter no of days lesser than B by A to complete work\n"); scanf("%f",&b); c=ab/(a-1); d=c-b; printf("no of days to complete work by A and B is %d",(c*d)/(c+d)); }

 Prabha said: (Mon, Sep 24, 2012 07:00:17 AM) If difference of time 2 days B takes 3 days Similarly why don't we take difference of time 60 days B takes 60*3 is 180 days. Please explain to me ?

 Joshi Sir said: (Wed, Nov 21, 2012 07:58:19 PM) Friends, don't make it complex: Here we go. Ratio of time taken by A & B = 1:3 And A takes 60 days less then B Suppose, days taken by B = x then days taken by A = (x - 60) Thus, A : B = (x - 60) : x 1 : 3 = (x - 60) : x 1/3 = (x - 60) / x X = 3 (x - 60) X = 3x - 180 180 = 3x - x 180 = 2x X = 180 / 2 = 90 Hence, Days taken by B = x = 90 days Days taken by A = (x - 60) = 90 - 60 = 30 days 1 day work of A and B = 1/30 + 1/90 = 4/90 = 2/45 So, Total days taken by A & B to complete the work = 45/2 = 22.5 days

 Ashutosh said: (Thu, Nov 29, 2012 04:45:15 PM) Formula-->nx- (n+1) /nx. 4x-4x/3=60 so x=45/2.

 Keerthi said: (Thu, Jan 10, 2013 10:20:09 AM) So by the explanation above we have to take in the ratio 1:3.

 Kavya said: (Thu, Jan 10, 2013 01:56:00 PM) A is twice as good a workmen as B and together they can finish a piece of work in 18days. In how many days will A alone finish the work? Can we solve the above problem using the formula k*x/k^2-1.

 Pankaj said: (Tue, Feb 5, 2013 02:43:08 PM) Let A takes x days to do the work alone Therefore days taken by b is (x+60). Now A is 3 times faster than B So no.of days taken by A will be 3 times less than B. So 3*x=(x+60) 2x=60 x=30 days //work done by A Work done by B=30+60=90 days. Now we can find work done together 1/30 +1/90 to get the answer.

 Monika said: (Mon, Feb 11, 2013 12:01:32 PM) We have a direct formula for these kind of questions .. i.e., Work done together is given by = (m*d)/(m^2 - 1), Where d is no of days taken by B and m is no of time A is faster than B, Therefore = (3*60)/(3^2-1) = 22.5.

 Praveen said: (Sun, Mar 10, 2013 08:08:47 PM) @All. Please refer to Sheetal's response as given below. Its the best and easiest way to solve such questions. PS:Thanks sheetal. "A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1. SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA. K * X / K'S SQUARE - 1 =3 * 60 / 9 - 1 =3 * 60 / 8 =180 / 8 =22.5 DAYS. AS MENTIONED OPTION B.

 Sridhar said: (Sun, Apr 28, 2013 02:32:53 PM) Simple way: A and B ratio 1:3. Since A finishes 60 days lesser than be A takes 90 days and B takes 30 days. So per day calculation (1/90+1/30) = 22.5 days.